Differentiate the following functions with respect to `x` : `tan^(-1){sqrt((1+cosx)/(1-cosx))}` , `0< x < pi`

Explanation

To differentiate the function \( y = \tan^{-1}\left(\sqrt{\frac{1 + \cos x}{1 - \cos x}}\right) \) with respect to \( x \), we can follow these steps:

### Step 1: Rewrite the Function
We start with the function:
\[ y = \tan^{-1}\left(\sqrt{\frac{1 + \cos x}{1 - \cos x}}\right) \]
Using the trigonometric identities:
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